New project: a smaller kayak

 Having just completed a large kayak with ample storage space, it weighed in at sixty pounds, which is too much for my wife.  But the basic design looks good, now I plan to create a slightly smaller version of the same exact design.  Frames will be spaced at 13.5" instead of 15" and the depth is reduced by 2.5".  I wonder how different the hull will be visually.  Progress will be slow because of the holidays, tax prep, and a long-planned trip.  Design dimensions are 153" by 26.6".

 A hint of what is to come:  The deck beams are laminated.  They all have the same curvature; thus, they could all be built on the same form.  The remaining parts of the frames are built from individual pieces that are half-lapped and then bonded together.  The plank that all the frames are resting on will be the future keel.  That keel will have a slight rocker by design.  My strongback, such as it is, consists of a ten-foot long 2X6 resting on two sawhorses.

Kayak frame completed.  After I have the bottom and topsides planked, then I will alter the deck beams to create a cockpit.

1) The offsets for all frames were mathematically calculated.  The shape of the plank keel and the bow entry & stern were also calculated.  The total length of the sheer and length at each frame connection, also calculated mathematically.  

2) Full size drawings of frames, bow & stern, and keel ends were drawn.  Most data points are only a few inches apart.

3)  Individual pieces were constructed from those drawings.  Midlines were marked on each frame for visual reference during assembly.

4)  Given that three points define a plane, each frame can only fit in one position defined by the keel and port & starboard sheer connections.  At bow and stern, additional rigid triangles are created by the bow, keel, and port & starboard sheer connections at the adjacent frames. This forces the port & starboard sheers to meet in a predetermined fixed relation.

5)  With epoxy and plenty of clamps, all connections only fit in one position, allowing assembly without use of a strongback form.  Planking can now proceed on this rigid underlying total frame.

Now I have started planking the hull.  With natural wood, each plank has to be considered individually.  Few are absolutely straight.  None are the 14+ feet long needed; thus, each requires a scarf joint.  I ran them all through a planer to get uniform thickness.  The initial planks all are positioned in the 1st projection of the hull form, meaning they all lie in one plane and can be laid straight without any taper.

But this is a triple chine hull (four projections); at the turn of the bilge, angles change several times, and intersection of planes required that planks located at the turn of the bilge be tapered and less than full length.  The taper was determined by clamping the future plank in place and then tracing the overlap from the inside of the hull as a guide for trimming.

No fasteners used; tomorrow I will bond this partial length plank in place with epoxy and plenty of clamps.  Instead of spiling, I clamped the proposed new 1.5" wide plank in place and then traced (inside the hull) with a pencil the overlap between the new plank and previous plank. This guidance was then used to trim the new plank to its tapered form.    

No strongback or forms used.  The plank keel, frames, and stems create a solid skeleton to build on.

Planking of the hull is complete except for finishing.  Next, I will concentrate on cleaning up the interior and finishing it.  Other tasks to consider are the sanding and filling of the hull exterior and planning the cockpit and decking.  Still, this is a nice milestone of completion where it really looks like a boat.

Three coats of varnish on the interior.  The exterior has been sand/fill/sand with a flowable epoxy paste. Now I am creating a contrasting pattern of decking planks.  The color difference will be enhanced when I start varnishing.  The darker planks are select alder wood.  Alder is normally known for its knots; this is select alder; no knots, but still there are variations in the grain structure which cause slight curves in these planks.  In a ten-foot plank, you may find 2-3 slight curves.

When you are laying multiple adjacent planks, you can't allow gaps due to this waviness.  Thus, each plank needs to be fitted to its position, slowing the process.

Finished planking the deck and fitting the cockpit edging.  Now it will be more filling any flaws and more sanding of the deck.  Then paint and varnish.

Paint and varnish added.  I am using all Epifanes products and am pleased with the results.  The seat is being varnished separately.  Now I need to get a light trailer to carry either two kayaks or a single rowboat.  Colorado has few lakes, and many are at altitude where they are covered by ice for almost half the year.  Most marine products I use need to be mail ordered.  But the low humidity is excellent for boat building.

Finishing the planked hull

 Now that I have a fully planked hull to look at, I am asking myself, "Is this a kayak or a canoe?  Dimensions are 27" by 170".  I wanted to make a somewhat wide and stable hull for my wife, but I think it has more freeboard than needed, which gives it a canoe look.  Whatever.  I have already bought the keel plank for a next build.

I will be turning the hull over for sanding, fill coating, and more sanding to get a smooth exterior.  Looking at the hull, it would be very difficult to realize that this is a developable surface hull.  Completely designed using the mathematical accuracy of developable projection; no strongback required, in the final step, instead of connecting all offsets on the hull frames with straight lines, they were connected using a smooth curve.  By sheathing that curve with narrow planks (1.5" wide), the result is a curvaceous hull.

Next comes the sanding: Random orbital with 80 grit discs.  My Porter-Cable sander is falling apart; time to replace it.

My goal is not to sand it completely smooth.  I want people to see that it is a wooden planked hull.  What you see here are spots where squeezed-out resin was wiped off the hull surface.

When planking the hull, I put a bead of epoxy paste on the edge of each preceding plank before adding the next plank.  That requires cleanup of the squeezed-out resin, but better that than a dry joint. When planking was complete, I used a disposable brush and un-thickened resin to fill any remaining small voids.  I then used a flowable resin mixture, thickened with WEST 407 fairing filler, and wiped the entire hull using a flexible plastic squeegee.

That was followed by progressive sanding: 60 grit, 80 grit, and 120 grit (by hand).  This wasn't as onerous as it seems, using my new DeWalt random orbital sander.  Repeated vacuuming and next I will wipe down the hull surface before putting on a coat of primer.

Changed my mind.  I was anxious to take on the deck sheathing.  First, I cleaned up resin blebs in the interior and put down three coats of Cetol plus a high gloss sealer coat on the interior.  Now, I am applying deck planks two at a time, port and starboard working toward the centerline.  I will be adding hull access ports fore and aft as the planking proceeds.

Then it will be time for a vacation break. 

We are looking at the hull from the stern.  The hull is not symmetrical fore and aft; the bow is actually slenderer than the stern.  With the plumb ends, the waterline is almost 14 feet long.  Next, I will create flush hatch covers for the fore and aft access openings.  Then install a raised edge on the cockpit and build a seat for the paddler.

Those lifting handles are just resting in place; I need to do a lot of finishing on them.  The deck has only had a rough sanding and will require further fill and smoothing.

Hatch covers and cockpit edging in place.  This is a stern view; my camera makes it look like this would be the more pointed bow, but that is just wide-angle distortion.  I love the flush hatches; am trying to decide what type of latching system to use without visual impairment.

Now, all I have to do is make a seat for the cockpit.  Done! (but not shown)

Next up:  Using the same design numbers, I am creating a smaller version of this hull: 10% shorter and 2.5 inches lower.  Progress will be slow due to the holidays and a planned trip.

Rules for Creating Developable Hull Surfaces

Assume we are working in a mathematical X,Y,Z coordinate system where X define length, Y defines width, and Z defines height.

1.  A straight line can be defined by two points in space or by one point and a constant slope.

2.  A curved line can be defined by an algebraic equation(s) relating X, Y, and Z to each other.

3.  Projections can be in the form of a plane, a cylinder, or a cone.  The cylinder and cone do not need to be circular in cross-section and do not need to form completely closed surfaces.

4.  A plane can be defined by holding one coordinate constant or by using a constant slope in space.

5.  A cylinder can be defined by constant slope projections from an algebraically defined curve.

6.  A cone is defined by projections from a single focal point to a defined curve or other series of selected points.

7.  Projections can be combined by using common ruling lines (lines which are defined in both adjacent projections).

8.  Surfaces can, thus, be built up by combining multiple projections.

9.  Surfaces can be combined by common predefined border lines (straight or curved) or by intersections, either calculated or by graphic solution.

10.  Locating a conic focal point close to a limiting curve or intersection will accentuate curvature in that localized area.  Be sure that is that what you want.

11a.  Cross section shapes (for frames) can be found by holding X constant and solving for Y and Z.

11b. Waterlines can be calculated by holding Z constant and solving for X and Y.

11c.  Longitudinal sections can be calculated by holding Y constant and solving for X and Z.

12.  Mathematical curves defining the relation between X to Y and X to Z can be separate equations.

13.  Lengthwise, a defined curve can be made up of differing segments as long as they have a common slope at the point of juncture.

14.  The easiest curve I have found to use is a parabolic or trajectory curve with coefficients chosen to create the length and curvature desired.  The slope at any point is easy to determine.  The length to any point along the curve can be calculated using a derived formula.

15.  When creating a hull form, defining the midships cross-section shape and major chine is almost always the favored place to start.

The general form of equation I use is the following: Y=B(1-X^/L^) where "^" indicates the term squared. Y is half width, X is length measured from amidships forward, B is the maximum beam, and L is the overall half length.

The exact equation used for the forward width of my kayak is Y=8.1(1-X^/67.5^) where Y is calculated every 7.5 inches from X=67.5 to X=0 resulting in values of Y=8.1, 7.7, 7.2, 6.5, 5.6.... and so on. Note that the decreases are 0.1, 0.4, 0.9, 1.6, 2.5 and so on until Y=0 at the completion of nine segmental computations (9^=81).  The slope at any point on the curve is (the change in Y multiplied by 2 then divided by the change in X).

Thus, the end slope of this curve is 2x8.1/67.5 or 0.24, this can also be expressed as a change of 0.9 inches in width for every 3.75 inches change in length.  At the end of every attempted curve of a wooden board, there is always a short segment at the end where no fulcrum exists to exert torque to continue the curve to the very end and the end piece is straight (but angled). 

I then add that short segment of straight line (wooden plank) to the end of my curve, resulting in an overall length of 71.25 inches and overall beam of 9.0 inches.  The result is the equation and width offsets for the major chine.

At this point, you have either figured the concept out or are totally confused; I will stop here.

Finalized kayak design. Work begins.

Calculating the length of a mathematically derived sheer curve.  If I used a programmable calculator, I could do these calculations in one step, but I routinely use a simple TI-36X which I bought years ago.  So, I need to do the calculations in a stepwise fashion.  It is a calculation I only use once per boat design, not worth spending too many resources on.

This equation for curve length was derived by calculus integration of the mathematical curve equation.  All my college engineering studies were not completely wasted.

 I am completely committed to the 170" long by 27.5" wide kayak design.  I have the keel plank roughed out and the bow and stern stem pieces also "roughed out".  These pieces are only in approximate shape and will be trimmed and detailed more later.  Next item will be a start on the ten frames.  Incorporating one inch of rocker at the bow and stern created some complication.  How will I ensure that the keel plank is held in the required position without using a building strongback?  

Part of that can be done by the type of support provided beyond simply sawhorses.  Additionally, I have completed calculations for the overall length of the sheer and its intersection with each frame.  With a double-ended hull and each frame fixed at the keel plus port & starboard sheer locations, all frames can only assume one position.  The entire frame will form a single "girder", at least in theory.

I have already drawn out the full-size patterns.  Not hard to do when the largest frame is less than 30" wide and 15" high.  The frames do not change when their spacing is altered.  

The deck beams are laminated from thin 'cut-off' scraps I have been saving for a few years.  I built a curved ladder to clamp the strips into a conforming curve.

Bow and stern pieces created from 2"X4" scraps.  At this point they are only roughed out.  I need to cut channels for the sheer and chine strips.  I used a half thickness lap and Titebond III to join the two pieces.

All the frame pieces have been cut to shape. but that is only a beginning.  I will be using a half lap when I start bonding the parts together.  With sixty pieces to fit, it will be a lot of fine cutting.

The six parts for frame #5 (of ten) positioned on the full-size paper template.  When more are ready, I will bond them with epoxy.  Then they will be trimmed and notched for the longitudinal strips.

A preliminary look at how the frames line up on the plank keel.  All pieces shown here are still unfinished, but it is motivational to see that the parts will fit together.  The keel is presently 0.5" thick; I plan to plane that down to 0.4".  I usually do that outside because it creates so much wood dust; however, we still have snow outside my shop door.  I have other details to keep busy with for a while.

Finally, the ten frames, two stems, two sheer strakes, and keel are sufficiently complete that assembly can begin.  I placed a straight 2X4 across two sawhorses and placed the keel centered atop that.  Then I clamped the central section of the keel to the 2X4.  Next, I placed a sawhorse under each end of the keel and added a few scrap wood pieces of the proper thickness to provide the desired rocker in the ends.  Next, each frame was bonded and clamped in its proper place, spaced at 15" centers.

Port and starboard sheer strakes had been created, cut to proper length, and each intersection with a frame had been marked according to the calculated curved length of the curve.  The calculation is amazingly accurate, hundredths of an inch, but my shop accuracy is only about 1/16".  With both strakes joining at the stem ends of the double-ended hull, there is less chance of distortion.  Unfortunately, after removing all the clamps, I see that frames #3 & 8 are about 1/4" out of alignment at sheer height.

With each frame fixed in place by the keel and port & starboard strakes (3 points define a plane), it was only a matter of having sufficient clamps to maintain that position until the epoxy hardened.  No fasteners have been required thus far.  This provides the basic framework for the entire hull.  I will add another strake at the turn of the bilge and outline the cockpit; then it will be time to start planking.

The only strongback needed has been a straight 2X4 (6-8 feet long) and some sawhorses.  Accurate measurements along the curved sheer strake made the difference.

I have plenty of clamps of all sorts.

After the clamps have been removed.  Starting to outline the cockpit.  Next, I will flip it over and add a stringer at the major chine.

Kayak frame with more details added. A cardboard pattern is clamped on the lower right.  That area is developable, thus, could be sheathed with a single plywood sheet, but that is not the alternative I have chosen.  This pattern simply gives me a better idea of how the planking should be laid out.

Stringer added.  Then it is time to fair all the frames and the stems, then create a shelf on the plank keel edge to support the garboard.  I use an angle grinder for fairing; the stems take some serious wood removal to get the proper taper.  For the edge of the plank keel, I use a router.  This time I used a full-size router, its weight made it easier to control; not as easily deflected by variations in the wood grain.  Near the ends of the keel, you are changing the angle and following a curve; thus, you need freehand control without a guide.

The intersection of the plank keel and the stem.  The edge of the plank keel has been routed to support an edge of the garboard plank, and the stem has been beveled to support the plank ends.

I have purchased some planks of knotty alder for the sheathing.  Why knotty alder?  1) It was cheap. 2) It was high quality; it looked somewhat like select alder. 3) After I rip it into 1/4" planks, I can scarf out any significant defects and knots. But we are taking a break before I get started on that next step.

Two months later and the break is over.  I have ripped the knotty alder into 0.2" thick planks, cut out the significant knots and other defects, and then scarfed the resulting pieces into 15 (so far) 15-foot-long planks.  With planks only 1.5" wide and my chop saw set at a 7-degree angle, it was easy to get consistent, smoothly beveled scarfs.  The knots were frequent enough that most of my 15-foot planks have multiple scarfs.  

Progress.  Planked up to the major chine.  These planks have been straight and full length.  The next planks will be more complicated, either tapered or curved.

As I create a new design, I am always asking myself what could be done differently.  When I look at this hull design (and after sitting in it), I feel like the deck should be 2.5" lower.  There is more foot space present than needed.  A lower deck would enhance paddling.  Also, the hull could easily be 10% shorter.  The changes would reduce weight and windage.  I do not want to reduce stability; this is not meant to be an advanced paddlers design.

The present hull will permit more stowage and allow a more relaxed seating position.  Every tradeoff is a compromise.

Getting close to completing sheathing the hull.  Then I will turn it over, lightly sand, then go over the hull with a flowable epoxy paste to fill seams and provide a smooth surface.  I'll let that cure while doing some finishing to the interior.  Then I will do final sanding on the exterior and start on the deck.

   

Starting a new design and build: Kayak

 Last summer, my wife and I stayed at an island resort in Bocas del Toro, Panama, which furnished us kayaks to use in the island-strewn surrounding ocean.  Since the region was a tropical bay, small waves were of local origin, wind-driven but not open ocean swells.  Anyhow, we enjoyed the experience, and my wife said, "Can you build me a kayak?"  Well, of course I can!

I built my first boat, a self-designed kayak, in 1975.  Not a great design, but very appropriate for our circumstances at that time.  Now I have the opportunity to do it again.  My wife, Dawn, and I will never be hard core kayakers.  What I have considered is something easy to store and transport, fairly stable, but also easy to paddle with a decent glide and directional stability.

Looking at the commercial roto-molded plastic kayaks, most are about 12 feet long and 2 1/2 feet wide.  I used those dimensions as a starting point.  My result, mathematically generated, will be about 12' 4" long and 28" wide with a waterline width of 23-24" depending on the load.  Height at the midships sheer of 12" and at the cockpit center of about 14" (cambered deck). With a waterline width that narrow, stability must come from a centerline flat, gentle deadrise, and then progressive steeper topsides.

Concerning length, I have spaced the frames (or molds) 12" apart.  A longer hull can be easily created by re-spacing the frames and redrawing the bow and stern entries.  My 1975 kayak was almost 16 feet long, but it was for two persons.

Progress will be slow.  We have other interests to deal with.  (My wife wants to re-paint some of our home spaces.)  Not a problem; we already have several boats.  Actually, buying a light trailer is another task to research.  I'll post some sketches soon. 

This photo shows an overhead sketch view and profiles of some of the frames.  There will be a one-inch rocker in the keel at both ends.  I don't need exact drawings here because a table of accurate dimensions was the first thing created.  Full-size frame patterns will be made from those dimensions.

How can this be a developable hull design when the frames are so smoothly curved?  The answer is that I intend to sheath the hull by strip planking.  Wider planks would result in a more faceted surface.  In a hull of such narrow width, planks by necessity need to be narrow to hug the curves.  I calculated many spaced points at each frame location and then connected them with a smooth curve.  If I had connected them with straight lines, you would see a faceted surface on this sketch.

Should I explain in detail the steps in this design?  I am thinking not; the design calculations are easy for me due to my experience, but it would get complicated to describe clearly in words.  I start by describing the major chine, then create a midships cross-section, find mathematical curves to fit the overall dimensions, and then create further projections to describe additional minor chines.  Finally, I describe the desired sheer location and the desired curve for a cambered deck (not shown).   

X is the length from bow toward stern calculated to the inside of sheathing.  Yc (width)and Zc (height) describe the major chine.  Y1,2,3 and Z1,2,3 describe the topsides projections, additional "chines". Ys and Zs describe the sheer location. 

This is a table of all values needed to make patterns for the eleven frames (or molds) excluding the cambered deck which will be on the next graph.  Note that between X=75 and 87 all the values are constant.  This is a parallel section and could be omitted for a smaller paddler.

First is the equation of the deck camber.  Next are the dimensions defining the bow and stern profiles.  The bow is a finer angle, 16.7 degrees, versus 20.5 for the stern profile.  Finally, we have the outline of the plank keel.  Total length is about 129.5 inches, 7.2 inches wide for about 77 inches of its center length. The included one inch of forward rocker extends the forward length of the keel with some curvature.  All dimensions are to the inside of the sheathing except the plank keel, since it serves as both frame and sheathing.  I have been using 0.5" lumber for the keel and consider 0.3" as exterior and any added thickness is part of the frame.

These two tables of dimensions will give me everything I need to build the kayak.  I will build a pattern for the deck profile which I can match up to the sheer beam at each frame.  After laying out the outline of each frame, I will design the frame elements and then can start a list of materials.

First thing purchased was the wood for the keel.  Needing 11 feet by about 7.5 inches by about 0.5 inch thick, I found two fairly straight boards, about 8' x 7.75" x 0.5".  By scarfing at a 5/1 angle (I usually use an 8/1 bevel) I ended up with about a 16' plank.  Looking at the keel plank and envisioning the total hull built with it as the foundation, I decided that the hull looked too short, with too much wasted keel plank.  So, I have decided to re-space the frames to a 15" interval resulting in a kayak about 14' 2.5" long.  Still a handy size which will fit on most light duty trailers.

I will be posting altered dimensions soon.  The twelve-footer would function okay, but by increasing the length and fineness, the bow half angle is reduced from 16.7 degrees to 13.5 degrees.  Should make it easier to plank.  Spanning 15" between frames with 1/4" planks, I will need to be careful in aligning the plank edges, but I have many clamps for that purpose.